The present invention relates to a divide method and apparatus for use in a data processing system.
In order to simplify the calculations in a divide apparatus, approximations of the given dividend and given divisor are employed so that inaccuracies may be introduced into the quotient.
In a known prior art method for improving the accuracy of an approximate reciprocal divisor, a 1st approximate reciprocal divisor is obtained from a lookup table by using the high-order bits of the normalized divisor as an address, and a second approximate reciprocal divisor is obtained by multiplying the 1st approximate reciprocal divisor by the two's complement of the product of the 1st approximate reciprocal divisor and the normalized divisor. That is, the 2nd approximate reciprocal divisor R.sub.1 can be obtained by EQU R.sub.1 =R.sub.0 .times.(2-D.sub.0 .times.R.sub.0)
where D.sub.0 is a normalized divisor, R.sub.0 is a 1st approximate reciprocal divisor, R.sub.1 is a 2nd approximate reciprocal divisor, .alpha. is a positive integer, and .vertline.1-D.sub.0 .times.R.sub.0 .vertline.&lt;2.sup.-.alpha.. In this case, the accuracy of the reciprocal of R.sub.1 is: ##EQU1##
The above method, however, requires two multiplications in order to obtain R.sub.1.
Further, in a prior divide apparatus in which a partial remainder is calculated in the form of a remainder multiplied by an approxiamte reciprocal divisor, and in which successive iterations are performed such that the higher order bits of the partial remainder become the partial quotient, the following case may happen. That is, in the case that a quotient is calculated up to the desired bits by using an approximate reciprocal divisor smaller than a correct reciprocal divisor, and that the dividend is assumed to be equal to the divisor, the quotient does not always become 1, but it becomes in a binary notation a number such as having 1's from below the radix point down to the lowest order bit. Thus, the quotient calculated by successive iterations may become smaller than the correct quotient by the lowest order bit 1, when compared down to the desired lowest bit. Therefore, if the product of the number obtained by adding 1 to the lowest order bit of the quotient calculated through successive iterations and the divisor is equal to or smaller than the dividend, then the number obtained by adding 1 to the lowest order bit of the quotient calculated through successive iterations is concluded as a final quotient. This, however, takes a fairly long time to check and correct the quotient.
One example of prior art divide methods and divide apparatuses is disclosed in U.S. Pat. No. 3,828,175.